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Ay benefit concert, twelve bands have volunteered to perform but there is only enough time for eight of the bands to play. How many lineups are possible?

Sagot :

facundo3141592

Answer:

There are 495 different lineups

Step-by-step explanation:

If we have a set of N elements, the total number of different combinations of K elements (such that K ≤ N) is given by:

[tex]C (N, K) = \frac{N!}{(N - K)!*K!}[/tex]

In this case, we have 12 bands, but we can only select 8 of them.

Then we have N = 12, and K = 8.

Using the above formula, we can conclude that the total number of possible lineups (combinations of bands) is:

[tex]C (12, 8) = \frac{12!}{(12 - 8)!*8!} = \frac{12!}{(4)!*8!} = \frac{12*11*10*9}{4*3*2} = 495[/tex]

There are 495 different lineups

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